Differentiate the functions given w.r.t. x:`sqrt(((x-1)(x-2))/((x-3)(x – InterviewSolution

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1.	Differentiate the functions given w.r.t. x:`sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`
Answer» Let `y = sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))` Taking log both sides, `=> lny = 1/2ln[((x-1)(x-2))/((x-3)(x-4)(x-5))]` Differentiating both sides w.r.t. x, `1/ydy/dx = 1/2[1/(x-1)+1/(x-2)-1/(x-3)-1/(x-4)-1/(x-5)]` `=>dy/dx = y/2[1/(x-1)+1/(x-2)-1/(x-3)-1/(x-4)-1/(x-5)]` `=>dy/dx = 1/2sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))[1/(x-1)+1/(x-2)-1/(x-3)-1/(x-4)-1/(x-5)]`

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